Importance of Stability

How do clearinghouses help stop unraveling? They can establish a thick market at an efficient time. We’ve conjectured that stability plays a role in helping them do this successfully. 2

Priority matching (an unstable system) Edinburgh, 1967No longer in use Birmingham 1966, 1971, 1978""" " Newcastle1970's""" " Sheffield 196x""" " In a priority matching algorithm, a 'priority' is defined for each firm-worker pair as a function of their mutual rankings. The algorithm matches all priority 1 couples and removes them from the market, then repeats for priority 2 matches, priority 3, etc. E.g. in Newcastle, priorities for firm-worker rankings were organized by the product of the rankings, (initially) as follows: 1-1, 2-1, 1-2, 1-3, 3-1, 4-1, 2-2, 1-4,

Priority matching (an unstable system) This can produce unstable matchings -- e.g. if a desirable firm and worker rank each other 4th, they will have such a low priority (4x4=16) that if they fail to match to one of their first three choices, it is unlikely that they will match to each other. (e.g. the firm might match to its 15th choice worker, if that worker has ranked it first...) After 3 years, 80% of the submitted rankings were pre-arranged 1- 1 rankings without any other choices ranked. This worked to the great disadvantage of those who didn't pre-arrange their matches.

5 What makes a clearinghouse successful or unsuccessful? A matching is “stable” if there aren’t a doctor and residency program, not matched to each other, who would both prefer to be. Hypothesis: successful clearinghouses produce stable matchings. How to test this?

6 MarketStableStill in use (halted unraveling) NRMP yesyes (new design in ’98) Edinburgh ('69)yesyes Cardiffyesyes Birminghamnono Edinburgh ('67)nono Newcastlenono Sheffieldnono Cambridgenoyes London Hospitalnoyes Medical Specialtiesyesyes (~30 markets, 1 failure) Canadian Lawyersyesyes (Alberta, no BC, Ontario) Dental Residenciesyes yes (5 ) (no 2) Osteopaths (< '94)nono Osteopaths (> '94)yes yes Pharmacistsyes yes Reform rabbisyes (first used in ‘97-98)yes Clinical psychyes (first used in ‘99)yes So stability looks like an important feature of a centralized labor market clearinghouse.

7 The need for experiments How to know if the difference between stable and unstable matching mechanisms is the key to success? –There are other differences between e.g. Edinburgh and Newcastle The policy question is whether the new clearinghouse needs to produce stable matchings (along with all the other things it needs to do like handle couples, etc. ) –E.g. rural hospital question…

8 A matching experiment (Kagel and Roth, QJE 2000) 6 firms, 6 workers (half "High productivity" half "low productivity") It is worth $15 plus or minus at most 1 to match to a high It is worth $5 plus or minus at most 1 to match to a low There are three periods in which matches can be made:-2, -1, 0. Your payoff is the value of your match, minus $2 if made in period -2, minus $1 if made in period -1 Decentralized match technology : firms may make one offer at any period if they are not already matched. Workers may accept at most one offer. Each participant learns only of his own offers and responses until the end of period 0. After experiencing ten decentralized games, a centralized matching technology was introduced for period 0 (periods -2 and -1 were organized as before). Centralized matching technology: participants who are still unmatched at period 0 submit rank order preference lists, and are matched by a centralized matching algorithm. Experimental variable: Newcastle (unstable) or Edinburgh (stable) algorithm.

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10 Offers and acceptances

What do the experiments add to the field data? They show that stable versus unstable clearinghouse organization is important, in a controlled environment in which this is the only difference. Demonstrates robustness: we’ve now seen the same phenomena in markets ranging in size from 20,000+ participants, to hundreds, to half a dozen. Suggests that the asymmetry between firms and workers—and the ability to reject (or delay) unwanted offers—plays a critical role.

12 MarketStableStill in use (halted unraveling) NRMP yesyes (new design in ’98) Edinburgh ('69)yesyes Cardiffyesyes Birminghamnono Edinburgh ('67)nono Newcastlenono Sheffieldnono Cambridgenoyes London Hospitalnoyes Medical Specialtiesyesyes (~30 markets, 1 failure ) Canadian Lawyersyesyes (Alberta, no BC, Ontario) Dental Residenciesyes yes (5 ) (no 2) Osteopaths (< '94)nono Osteopaths (> '94)yes yes Pharmacistsyes yes Reform rabbisyes (first used in ‘97-98)yes Clinical psychyes (first used in ‘99)yes Lab experimentsyesyes. (Kagel&Roth QJE 2000)nono Lab experiments fit nicely on the list, just more of a variety of observations that increase our confidence in the robustness of our conclusions, the lab observations are the smallest but most controlled of the markets on the list…

13 The Roth-Peranson algorithm is also used in other market clearinghouses since 1998 Postdoctoral Dental Residencies in the United States Psychology Internships in the United States and Canada Neuropsychology Residencies in the United States and Canada Osteopathic Internships in the United States Pharmacy Practice Residencies in the United States Articling Positions with Law Firms in Alberta, Canada

14 NRMP also runs Fellowship matches through the Specialties Matching Service (SMS) (using the Roth-Peranson algorithm since 1998) Abdominal Transplant Surgery (2005) Child & Adolescent Psychiatry (1995) Colon & Rectal Surgery (1984) Combined Musculoskeletal Matching Program (CMMP) –Hand Surgery (1990) Medical Specialties Matching Program (MSMP) –Cardiovascular Disease (1986) –Gastroenterology ( ; rejoined in 2006) –Hematology (2006) –Hematology/Oncology (2006) –Infectious Disease ( ; rejoined in 1994) –Oncology (2006) –Pulmonary and Critical Medicine (1986) –Rheumatology (2005) Minimally Invasive and Gastrointestinal Surgery (2003) Obstetrics/Gynecology –Reproductive Endocrinology (1991) –Gynecologic Oncology (1993) –Maternal-Fetal Medicine (1994) –Female Pelvic Medicine & Reconstructive Surgery (2001) Ophthalmic Plastic & Reconstructive Surgery (1991) Pediatric Cardiology (1999) Pediatric Critical Care Medicine (2000) Pediatric Emergency Medicine (1994) Pediatric Hematology/Oncology (2001) Pediatric Rheumatology (2004) Pediatric Surgery (1992) Primary Care Sports Medicine (1994) Radiology –Interventional Radiology (2002) –Neuroradiology (2001) –Pediatric Radiology (2003) Surgical Critical Care (2004) Thoracic Surgery (1988) Vascular Surgery (1988)